Suppose there was a bus, and the bus has a regular size boxing glove on the front of it. And the bus is driven at whatever speed, and it hits a ball. And it hits it with a force greater than what somebody can achieve by just throwing a punch.

Scenario B-

Suppose there was a bus, going the same speed as in scenario A, but with no boxing glove on the front, and the bus has a person strapped on the front, and the person has a boxing glove, and punches the ball.

The question is,
will the ball go further in scenario A, or scenario B?

I'm not sure because I wonder if the arm is going to absorb more than it adds?

It all depends what you mean by "and the person has a boxing glove, and punches the ball."

If the person's punch involves moving his fist forward at the moment of impact relative to the bus, then the velocity of the boxing glove relative to the ball is greater in scenario B than in scenario A. So it would seem that the ball goes further in scenario B. However ... if the ball is sufficiently massive it may be that the person's arm strength is overwhelmed, so that the at the moment of impact the persons fist actually moves backward relative to the bus - in effect the person's arm absorbs some of the energy of the impact, in which case the ball moves slower in scenario B, and hence goes a shorter distance. Bottom line is: it depends.

It all depends what you mean by "and the person has a boxing glove, and punches the ball."

If the person's punch involves moving his fist forward at the moment of impact relative to the bus, then the velocity of the boxing glove relative to the ball is greater in scenario B than in scenario A. So it would seem that the ball goes further in scenario B. However ... if the ball is sufficiently massive it may be that the person's arm strength is overwhelmed, so that the at the moment of impact the persons fist actually moves backward relative to the bus - in effect the person's arm absorbs some of the energy of the impact, in which case the ball moves slower in scenario B, and hence goes a shorter distance. Bottom line is: it depends.

The ball is not massive or very heavy, and could be punched without the bus.

e.g. suppose it's a tennis ball.

I wonder if maybe the force created by the bus will be a lot of force for the arm and overwhelm it a little bit.. and that while the arm won't move back, maybe it will absorb some of the force of the bus.

Could that happen even if it's hitting e.g. a tennis ball?

Like would greater force from the bus have a similar effect on the arm, as a bigger ball i.e. causing the arm to absorb force on striking?

Like, If you had to punch a ping pong ball , and the ping pong ball was built well so it won't break, but you were on the front of a bus moving so fast like near the speed of sound, then perhaps your arm would feel quite a collision with the ball?

Given how light a tennis ball is it seems obvious that punching at the ball will give it more kinetic energy than simply letting the ball hit the glove and bounce off. Think of it like this: a bus going at 60 MPH and hitting a ball is analogous to a bus standing still and being hit by a ball going at 60 MPH. You can probably visualize that if you throw a tennis ball at a boxing glove the glove absorbs much of the kinetic energy of the ball - this is your scenario A. But if you throw a ball at someone wearing a boxing glove who punches it back at you (scenario B), the ball will come off the face of the glove at a higher return velocity than under scenario A, because some of the KE of the moving glove is imparted into the ball.

To put it in real simple terms: would you rather be hit in the face by a boxer who can hit you with his gloved fist at 60MPH, or 90MPH?

Given how light a tennis ball is it seems obvious that punching at the ball will give it more kinetic energy than simply letting the ball hit the glove and bounce off. Think of it like this: a bus going at 60 MPH and hitting a ball is analogous to a bus standing still and being hit by a ball going at 60 MPH. You can probably visualize that if you throw a tennis ball at a boxing glove the glove absorbs much of the kinetic energy of the ball - this is your scenario A. But if you throw a ball at someone wearing a boxing glove who punches it back at you (scenario B), the ball will come off the face of the glove at a higher return velocity than under scenario A, because some of the KE of the moving glove is imparted into the ball.

To put it in real simple terms: would you rather be hit in the face by a boxer who can hit you with his gloved fist at 60MPH, or 90MPH?

Let's say the bus goes at 60mph and the arm at 20mph, and the arm decelerates on impact with the tennis ball. How much would the arm have to decelerate in order for the impact to be greater without the arm?